Comparison of Field-Oriented Control and Direct Torque Control for Permanent Magnet Synchronous Motor (PMSM)

Transcription

1 Worl Acaemy of Scence, Engneerng an Technology Comparson of Fel-Orente Control an Drect Torue Control for Permanent Magnet Synchronous Motor (PMSM) M. S. Merzoug, an F. Nacer Abstract Ths paper presents a comparatve stuy on two most popular control strateges for Permanent Magnet Synchronous Motor (PMSM) rves: fel-orente control (FOC) an rect torue control (DTC). The comparson s base on varous crtera nclung basc control characterstcs, ynamc performance, an mplementaton complexty. The stuy s one by smulaton usng the Smulnk Power System Blockset that allows a complete representaton of the power secton (nverter an PMSM) an the control system. The smulaton an evaluaton of both control strateges are performe usng actual parameters of Permanent Magnet Synchronous Motor fe by an IGBT PWM nverter. Keywors PMSM, FOC, DTC, hysteress, PWM. I. INTRODUCTION ERMANENT magnet (PM) synchronous motors have P attracte ncreasng nterest n recent years for nustral rve applcaton. The hgh effcency, hgh steay state torue ensty an smple controller of the PM motor rves compare wth the nucton motor rves make them a goo alternatve n certan applcatons. Moreover, the avalablty of low-cost power electronc evces an the mprovement of PM characterstcs enable the use of PM motors even n some more emanng applcatons [1]. It s now recognze that the two hgh-performance control strateges for PMSM are fel-orente control (FOC) an rect torue control (DTC). They have been nvente respectvely n the 70 s an n the 80 s. These control strateges are fferent on the operaton prncple but ther objectves are the same. They am both to control effectvely the motor torue an flux n orer to force the motor to accurately track the comman trajectory regarless of the machne an loa parameter varaton or any extraneous sturbances. Both control strateges have been successfully mplemente n nustral proucts. The supporters of fel-orente control an rect torue control clam the superorty of ther strategy versus the other. Up to now, the ueston has not been clearly answere. The purpose of ths paper s to present a comparatve stuy on these two control strateges n orer to clarfy the myth. The comparson s base on varous crtera nclung basc control characterstcs, statc an ynamc performance, an mplementaton complexty []. II. THE MODEL OF PMSM The electrcal an mechancal euatons of the PMSM n the rotor reference (- ) frame are as follows [7]: R L s I = I + ωr I + V t Rs 1 I I ω I ϕ ω V t = L L L + r f r I f (1) ϕ = + ϕ () ϕ () = LI An the electromagnetc torue C e s gven by: Ce = P[( L ) I I + Iϕ f )] (4) The euaton for the motor ynamcs, on the other han, s Ω C C C = J (5) t e r f ω = PΩ (6) Fg. 1 presents the moel of PMSM n - axs: Fg. 1 Functonal schema of the Park moel III. DESCRIPTION OF FIELD-ORIENTED CONTROL AND DIRECT TORQUE CONTROLS SCHEMES A. Fel-Orente Control System The prmary prncple n controllng a PMSM rve s base on fel orentaton. Snce the magnetc flux generate from 99

2 Worl Acaemy of Scence, Engneerng an Technology the PM rotor s fxe n relaton to the rotor shaft poston, the flux poston n the coornates can be etermne by the shaft poston sensor. In (), f I = 0, the -axs flux lnkageϕ s fxe. Snce ϕ f s constant for a PMSM, the electromagnetc torue s then proportonal to I whch s etermne by close-loop control [8]. Ce = Pϕ fi (7) Hence the representaton follows: [4] C = (8) e kt I an more popular nowaays. The basc ea of DTC for nucton motor s to control the torue an flux lnkageby selectng the voltage space vectors properly, whch s base on the relatonshp between the slp freuency an torue. In the late 1990's, DTC technues for the Permanent Magnet Synchronous Machne (PMSM) machnes have appeare [4]. Fg. 4 shows a rect torue controlle PMSM rve system. Where: kt = Pϕ f (9) The rotor flux s prouce only n the axs whle the current vector s generate n the axs n the fel-orente control. Snce the generate motor torue s lnearly proportonal to the -axs current, as the -axs rotor flux s constant n (), the maxmum torue per ampere can be acheve []. Hysteress PWM Current Control Hysteress current control s a PWM technue, very smple to mplement an takng care rectly for the current control. The swtchng logc s realze by three hysteress controllers, one for each phase. Fg. The hysteress PWM current control, also known as bangbang control, s one n the three phases separately. Each controller etermnes the swtchng-state of one nverter halfbrge n such a way that the corresponng current s mantane wthn a hysteress ban Δ [9]. * a * b * c a b c Swtchng logc I 1/U 1/U Hysteress ban Current reference Real courant Output voltage Fg. Hysteress PWM, current control an swtchng logc The confguraton of a fel-orente PMSM rve system wth conventonal cascae poston an spee control s shown n Fg.. B. Drect Torue Control system Snce M. Depenbrock an I. Takahash propose Drect Torue Control (DTC) for nucton machnes n the mle of 1980 s, more than one ecae has passe. It s gettng more Fg. System confguraton of fel-orente PMSM Estmaton of the Torue an the flux Lnkage The basc prncple of the DTC s to select proper voltage vectors usng a pre-efne swtchng table. The selecton s base on the hysteress control of the stator flux lnkage an the torue. In the basc form the stator flux lnkage s estmate wth: [5] t s ()= t Vs RsIs t+ s 0 ( ) 0 ϕ ϕ (10) Where ϕ 0 s the ntal value of the stator flux lnkage. Let us replace the estmate of the stator voltage wth the true value an wrte t as: j π/ j4 π/ VS ( SA; SB; SC) = U0 ( SA + SBe + SCe ) (11) Sa, Sb an Sc represent the states of the three phase legs 0 meanng that the phase s connecte to the negatve an 1 meanng that the phase s connecte to the postve leg. 00

3 Worl Acaemy of Scence, Engneerng an Technology The stator current space vector s calculate from measure currents,, : A B C J π/ j4 π/ S = ( A + Be + Ce ) (1) ϕs θs = arctg ϕ β Sα The torue can then be estmate wth: (15) Fg. 4 System agram of a typcal DTC PMSM rve system The voltage vectors obtane ths way are shown n Fg. 5. Ce = P ( ϕsα ISβ ϕsβisα ) (16) The voltage vector plane s ve nto sx sectors so that each voltage vector ves each regon nto two eual parts. In each sector, four of the sx non-zero voltage vectors may be use. Also zero sectors are allowe. All the possbltes can be tabulate nto a swtchng table (Table I). The output of the torue hysteress comparator s enote as τ, the output of the flux hysteress comparator as φ an the flux lnkage sector s enote as θ. The torue hysteress comparator s a three value comparator. τ = 1 means that the actual value of the torue s abovethe reference an out of the hysteress lmt, an τ = 1 means that the actual value s below the reference an out of the hysteress lmt. The flux hysteress comparator s a two value comparator. φ = 0 means that the actual value of the flux lnkage s above the reference an out of the hysteress lmt an φ = 1 means that the actual value of the flux lnkage s below the reference an out of the hysteress lmt [6]. TABLE I SWITCHING TABLE PRESENTED BY TAKAHASHI AND NOGUCHI θ, τ, φ θ 1 θ θ θ 4 θ 5 θ 6 τ = 1 V V V 4 V 5 V 6 V 1 φ = 1 τ = 0 V 7 V 0 V 7 V 0 V 7 V 0 τ = 1 V 6 V 1 V V V 4 V 5 φ = 0 τ =1 V V 4 V 5 V 6 V 1 V τ = 0 V 0 V 7 V 0 V 7 V 0 V 7 τ = 1 V 5 V 6 V 1 V V V 4 Fg. 5 Voltage vectors for DTC The composte α an β of vectorϕ s can be obtane: ϕ ( ) = V R I t Sα Sα S Sα 0 ( ) ϕsβ = VSβ RSISβ t 0 Stator flux lnkage wrtten: The angle θ S s eual to: t t ( ) ( ) (1) ϕ = ϕ + ϕ (14) s Sα Sβ IV. COMPARISON OF STATIC AND DYNAMIC PERFORMANCE In ths secton, statc an ynamc performances of FOC an DTC schemes are obtane by smulaton usng the MATLAB/ Smulnk Power System Blockset. Snce the objectve of the work s to compare the control strateges, the same power secton s use n both systems. It s necessary to make a comparson of statc an ynamc characterstcs of both techncal comman an uner the same operatng contons (reference, charges sturbance etc.), an n the same confguraton smulaton (step samplng, tme smulaton,) In ths paper we wll present the avantages an savantages of each type of comman, better comman wll be the one that best meets the reurement to know: Best performance statc an ynamc. Best prosecuton guelnes control. 01

4 Worl Acaemy of Scence, Engneerng an Technology Best releases sturbance. Insenstvty to changes n parameters. A. Comparson at the level of regulaton spee Fg. 6 llustrates the smulaton results of both techncal comman FOC hysteress an the DTC, where to apply a torue loa eual to 5N.m at t = 0.1s an a reference spee eual to 100 ra /s. It s note that the FOC hysteress presents a peak torue at startup larger than the DTC, an a torue of uck response ue to applcaton of the loa at t = 0.1s, whch allows the rap rejecton of the sturbance. At spee, we can see that the DTC has a hgh ynamc wthout overshoot, start-up, an the response tme are reuce compare to the FOC hysteress. For the answer stator flux, t reaches ts reference value wthout overrun for the DTC, aganst the FOC hysteress there s an overrun at startup. B. Test of Strength for Reversng Rotaton of the Machne To test the robustness of both techncal comman at the reverse recton of rotaton, t ntrouce a change n recor spee reference +100 ra/s to -100 ra /s tme t=0.1s after a torue loa eual to Nm. In Fg. 7, we can say that the contnuaton n spee s normally an wthout overrun for both techncal commans (DTC an FOC). It notes that the FOC hysteress presents a peak torue than the DTC. C. Test of Robustness for Loa Change Fg. 8 represents spee, torue an Flux stator of the machne n case starter vacuum an a level of spee eual to 100ra /s. At the moment t = 0.1s she apples a loa torue eual to 5N.m, then at t = 0.15s applyng a loa torue eual to 0N.m, we fn that the Torue respons nstantly, an that ts spee reaches Reference after a small eformaton reaches ts reference after a small eformty n the case of FOC. By cons n the case of DTC spee reaches ts reference after a conserable stran. The trajectory of the flux n ( α, β ) reference s crcular. V. COMPARISON BETWEEN THE DTC AND THE FOC The DTC oes not necesstate any mechancal measure such as the one of spee or poston of the machne; of more the senstveness to the machne parameters clearly s lessene n the case of the DTC, snce the flow estmaton s one accorng to a sngle parameter to know the resstance stator. In aton, PWM s replace, n ths orer by a smple table of commutaton whch the return, so much easer. The orer DTC has for avantages: The reucton of the tme of response of the couple. The harness n comparson wth the varaton of the parameters of the machne an nutrton. The rect mposton of the ampltue of the unulatons of the couple an flow. She aapts herself by nature to the absence of sensor Mechancal connecte to the tree motor. She presents major problems: The absence of mastery of the harmonc ones of couple. The check vector by orentaton of the flux rotorue FOC was evelope to elmnate nternal couplng of the machne, provokng varatons of the flux lnkage to the Torue. The control vector by orentaton of the flux rotorue presents a number of avantages: To allow a ecouplage between the flux an the torue rather smple, thus a we beach of spee. An a number of nconvenences: Weak harness to the varatons Parametrc an n partcular to the one of the constant one of tme rotorue. Necesstate of a moulaton one for the orer come close to the nverter that provokes elays, especally own wth freuency of moulaton. (a) (b) Fg. 6 Regulaton of spee followe by an applcaton of torue loa at the t = 0.1 s 0

5 Worl Acaemy of Scence, Engneerng an Technology Table II, summary a comparatve stuy of the performances between the orer FOC an the DTC: TABLE II COMPARISON OF FOC AND DTC SCHEMES FOC DTC Transformaton Present Vo Dynamcs hgh hgh Robustness Robust Robust Spee sensor Necessary Less necessary Parameter senstvty Bg Average Control close Necessary PWM Not of PWM Découplage Necesstate Natural Regulators Behavor own spee orentaton Three stator regulator (Hysteress) Goo - Torue regulator - Flux regulator not goo (a) FOC (b) DTC Fg. 7 Comparson of nverson spee (100ra/s, 100 ra/s) TABLE III PARAMETERS OF THE PMSM USED IN THIS PAPER Rate output power 1500 Wat Magnetc flux lnkage web Poles Stator resstance 1.4 Ω -axs nuctance H -axs nuctance H Inerta KG.M frcton Cœffcent N.M.S/ ra VI. CONCLUSION In ths paper, man characterstcs of fel-orente an rect torue control schemes for PMSM rves are stue by smulaton wth a vew to hghlghtng the avantages an savantages of each approach. It s ffcult to clearly state on the superorty of DTC versus FOC because of the balance of the merts of the two schemes. We one conclue that the vector orer t better s aapte (loa varaton), an the responses wth the DTC are ucker. (a) FOC (b) DTC Fg. 8 Comparson at the varaton torue loa REFERENCES [1] C. Maemls, V. G. Agels, "On Conserng Magnetc Saturaton wth Maxmum Torue to Current Control n Interor Permanent Magnet Synchronous Motor Drves," IEEE Trans. Energy Converson, vol. 16, no., Sep [] H. L. Huy, "Comparson of Fel-Orente Control an Drect Torue Control for Inucton Motor Drves," X/99/$ IEEE. [] K. K. Shyu, C. K. La, Y. W. Tsa, an D. I. Yang, "A Newly Robust Controller Desgn for the Poston Control of Permanent-Magnet Synchronous Motor," IEEE Trans on Inustral Electroncs. vol. 49, no., Jun. 00. [4] L. Tang, L. Zhong, M. F. Rahman an Y. Hu, "A Novel Drect Torue Control for Interor Permanent Magnet Synchronous Machne Drve System wth Low Rpple n Torue an Flux-A Spee Sensorless Approach" /0/$ IEEE. [5] M. F. Rahman, L. Zhong, E. Haue, an M. A. Rahman, "A Drect Torue-Controlle Interor Permanent-Magnet Synchronous Motor 0

6 Worl Acaemy of Scence, Engneerng an Technology Drve Wthout a Spee Sensor " IEEE Trans. Energy converson, vol. 18, no. 1, Mar. 00. [6] J. Luukko "Drect torue control of permanent magnet synchronous machnes analyss an Implementaton" Lappeenranta 000. [7] P. Pragasan, an R. Krshnan, "Moelng of permanent magnet motor rves" IEEE Trans. Inustral electroncs, vol. 5, no.4, nov [8] G. Grellet et G. Clerc, "Actuators electrc Prncpe / moel / control ". Eyrolles,.(n e.) 000, pp [9] F. Labrue, H. buyse, G. seguer an R. Bausère, "Converters power electroncs comman an ynamc behavor " vol. 5, 1998, pp